# induced emf when a wire or coil travel through a magnetic field

I've recently learned that If you move a conductor through a magnetic field, an emf is induced across the ends of the conductor:

$E = BLv$

I've also been told that the same is true for a coil but that the equation is:

$E = BLvN$

And that for a coil, there is only an emf induced when the current is entering or leaving the magnetic field as once the coil is inside, there is no change in magnetic flux linkage. I've been told that this is not the case with just a wire moving through a magnetic field, but I haven't been told why and I can't seem to figure it out.

I've thought about it, and I think it perhaps has something to do with the area covered by the wire moving at speed $v$ per unit time compared to the area covered by a coil moving at the same speed $v$ in the same unit time.

Unfortunately, I can't quite work it out.

Thank you.